Bayesian-optimized explainable machine learning framework for predicting reinforced concrete beam ultimate load-carrying capacity

Abstract

Accurate prediction of ultimate load-carrying capacity (failure load) of reinforced concrete (RC) beam is important for structural assessment, preliminary design, retrofit planning and decision support. Conventional empirical and code-based approaches are still useful, but they have a tendency to reduce the complexity of the nonlinear interaction of geometry, reinforcement, and material properties. This study proposed a Bayesian-optimized machine learning framework for predicting RC beam ultimate load-carrying capacity (failure load) using tabular engineering data and also converting the final predictor in the form of a readable graphical user interface. The dataset included 3234 records of the beam with nine input variables representing the beam geometry, concrete grade, ratio of longitudinal reinforcement, stirrup details, steel yield strength and concrete compressive strength with the target response being the ultimate load-carrying capacity (failure load) in kN. Seven regression models, that is, Linear Regression, Support Vector Regression, Decision Tree Regressor, Random Forest Regressor, Gradient Boosting Regressor, Extreme Gradient Boosting and Multilayer Perceptron were trained and compared using 80:20 train-test split and 5-fold cross validation with Hyperparameter optimization (Bayesian Optimization) Model performance was assessed in terms of \(R^2,\) RMSE, MAE, and MAPE and SHAP analysis was employed for the interpretation of the best-performing model. The results indicated that the Multilayer Perceptron had the highest predictive accuracy with the test \(R^2\) of 0.9992, RMSE of 21.3059 kN, MAE of 17.0777 kN, and MAPE of 0.4570%, which was better than all the competing models. Gradient Boosting Regressor and Extreme Gradient Boosting appeared to be the second best group while the Decision Tree Regressor showed the weakest generalization. SHAP interpretation showed that the most important predictors were longitudinal reinforcement ratio, beam width, beam height, concrete compressive strength and concrete grade with approximately 99.73% of global importance in the final model. The developed graphical user interface serves as a proof-of-concept tool to demonstrate the practical usability of the trained machine learning model for rapid prediction of reinforced concrete beam ultimate load-carrying capacity. The interface is intended primarily for preliminary assessment, educational demonstration, and exploratory analysis, rather than as a direct substitute for code-based structural design procedures. The results of the study show that a carefully optimized and interpretable machine learning framework can provide highly accurate and practically deployable prediction of RC beam ultimate load-carrying capacity (failure load) for structural engineering applications.